Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow

Details Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow

2005-10-27

arxiv.org/abs/quant-ph/0510211v1

Physics

Quantum Physics

17 pages, no figure

Scientific paper

We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties.

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